Beattie - Bridgeman

The equation fails badly at very high pressures, but for very low pressures the eq can be expanded intg the virial form as explained in Ref 8e 

The BB equation is also listed in Ref 8, p 69 but in a different form. It was claimed that it applies a correction for reduction of 

Beattie O.C. Bridgeman equation of state was first described in ProcAmAcadSci 63, 229(1928), which we did not consult One of the modifications of Beattie Bridgeman equation is given under Su  

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Kinetic considerations always lead to an equation of state giving the pressure as a function of the concentration and temperature, but for many purposes it is more convenient to know the molal volume as a function of the pressure and temperature. Beattie1 has indicated how the constants of an equation, similar in form to the Beattie-Bridgeman equation,2 may be obtained from p,V,T data. Often, however, the labor of this determination is not compensated by the added convenience. 

Beattie1 has also shown how an approximation sufficient for many purposes may be obtained making use of the constants already obtained for the Beattie-Bridgeman equation. The treatment is the same for any equation which may be expressed in the virial form. So expressed the Beattie-Bridgeman equation has four terms ... 

Generalized Beattie-Bridgeman Equation of State for Real Gases. It is written by Su Chang as ... 

Su Chang stated that their equation falls into the general form of the Lorentz Equation of State (qv). It may also be regarded as a simplified, generalized form of Beattie-Bridgeman Equation of State (qv)... 

W2) Wobl Equation of State. It is the 4th degree in the volume virial equation proposed in 1914 by Wohl and described in Addnl Ref Aj. it was used by Joffe (Ref 2a) far calcn of parameters of some gases in order to compare the results with those obtd by using the eq (5) of Joffe with equation of Beattie-Bridgeman and vanderWaals Joffe gives (Ref 2a, p 541) for Wohl equation ... 

The early application of volumetric data for hydrocarbons made use of the perfect gas laws. They were not sufficiently descriptive of the actual behavior to permit their widespread use at pressures in excess of several hundred pounds per square inch. The need for accurate metering aroused interest in the volumetric behavior of petroleum and its products at elevated pressures. Table II reviews references relating to the volumetric behavior of a number of components of petroleum and their mixtures. For many purposes the ratio of the actual volume to the volume of a perfect gas at the same pressure and temperature has been considered to be a single-valued function of the reduced pressure and temperature or of the pseudo-reduced (38) pressure and temperature. The proposals of Dodge (15), Lewis (12), and Brown (8) with their coworkers serve as examples of the nature of these correlations. The Beattie-Bridgeman (2) and Benedict (4) equations of state describe the volumetric behavior of many pure substances and their mixtures with an accuracy adequate (31) for most purposes. However, at pressures above 3000 pounds per square inch the accuracy of representation with existing constants leaves something to be desired. 

Beattie-Bridgeman (deton) equation of state 4D271... 

Equations of state (detonation and expin), listing of Abel, Allan, Beattie-Bridgeman, Becker, Becker-Kistiakowsky-Wilson, Benedict-Webb-Rubin, Berthelot, Boltzman, Brinkley-Wilson, Caldirola Paterson, Callendar,... 

The Beattie-Bridgeman equation, like most equations of state, is explicit in pressure. Certain calculations require an equation that is explicit in volume. Therefore, Beattie rearranged the Beattie-Bridgeman equation and modified it to give the following form. 

The constants are the same as for the Beattie-Bridgeman equation and the same numerical values may be used. The equation is less accurate than the Beattie-Bridgeman equation, but the agreement with the observed data is satisfactory. 

Both the Beattie-Bridgeman equation and the Beattie modification have been used with good accuracy at densities up to 2/3 of the critical density of the gas. Unfortunately, this does not cover the entire range of interest of die petroleum engineer. 

EXAMPLE 4-2 Calculate the molar volume of the gas given below at 100°F and 250 psia. Use the Beattie modification of the Beattie-Bridgeman equation. 

Third, use Beattie modification of the Beattie-Bridgeman equation to compute molar volume. 

Repeat Exercise 4-2. Use the Beattie-Bridgeman equation of state. 

A laboratory cell with volume of 0.007769 cu ft contains 0.001944 lb moles of the mixture given in the table below. Temperature is to be raised to 80°F. Calculate the pressure to be expected. Use the Beattie-Bridgeman equation of state. Compare your answers with experimental results of 1200 psia 2%. 

The permselectivity for membrane separations can also be calculated by substituting fugacities calculated from an equation of state, here using the Beattie-Bridgeman equation, into Equation (3) for the partial pressure values (4). The values of the permselectivities in Table IV are relatively constant at a fixed feed composition in agreement with the approximately linear behavior noted in Figures 9-11. 

This assumption is a good one at present day pressures of 500-800 psia for solids however, proposed operating pressures of 2000-3000 psia even at the temperatures of concern, may require some correction to the perfect gas law. Under these conditions, one should use the Beattie-Bridgeman or van der Waal s equation for the state equation and fugacity coefficients in the equilibrium calculations. 

Other semiempirical equations of state can be used to predict Joule-Thomson coefficients. Perhaps the best of these is the Beattie-Bridgeman equation, which can be written (for 1 mol) as... 

Plot the Leimard-Jones potentials for each of the gases studied. Obtain ft from Eqs. (16)-(18) by numerioal integration and compare the values from this two-parameter potential with those from the van der Waals and Beattie-Bridgeman equations of state. Optional A simple square-well potential model can also be used to eradely represent the interaction of two molecules. In place of Eq. (18), use the square-well potential and parameters of Ref. 6 to ealeulate /t. Contrast with the results from the Lennard-Jones potential and comment on the sensitivity of the calculations to the form of the potential.]... 

C. Solve the Dieterici, van der Waals, Beattie-Bridgeman, and Redlich-Kwong... 

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